This paper presents an efficient approach to the classification of the affine equivalence classes of cosets of the first order Reed-Muller code with respect to cryptographic properties such as correlation-immunity, resiliency and propagation characteristics. First, we apply the method to completely classify with this respect all the 48 classes into which the general affine group AGL(2,5) partitions the cosets of RM(1, 5). Second, after distinguishing the 34 affine equivalence classes of cosets of RM(1, 6) in RM(3,6) we perform the same classification for these classes.